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Proof step 82 from proof leninv-succ (previous step)

# nσ = ∞, nσ[m1] = m0 - 1, nσ[m] + 1 < m0, m1 < m2, stutf(nσ), ∀ m0. m < m0 → nσ[m0] = nσ[m] + 1 ⊦ nσ[m2] = m0 - 1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 83:
# nσ = ∞, nσ[m1] = m3, m0 = m3 + 1, m1 < m2, nσ[m] + 1 < m0, stutf(nσ), ∀ m0. m < m0 → nσ[m0] = nσ[m] + 1 ⊦ nσ[m2] = m3, m0 = 0

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m0, m3]

Additional information

Used simplifier rules: n0 < n ⊦ ¬ m + (* n) < (* n0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m0, m3